X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-common.tex;h=74a0fe508d22b44d82348ee767469272b7aa9f0d;hb=2dac5ec377a12619d1e1f7d8e036dab13af101cb;hp=408ca3310e7dbff8e498936e4bfefbe77e49c483;hpb=2b6f9aa58154ba0d7d25a94f7f74674139b5ac92;p=mjotex.git

diff --git a/mjo-common.tex b/mjo-common.tex
index 408ca33..74a0fe5 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -2,6 +2,12 @@
 % Only the most commonly-used macros. Needed by everything else.
 %
 
+% Needed for \mathbb.
+\usepackage{amsfonts}
+
+% Needed for \bigtimes.
+\usepackage{mathtools}
+
 % Place the argument in matching left/right parntheses.
 \providecommand*{\of}[1]{ \left({#1}\right) }
 
@@ -23,12 +29,21 @@
 % A pair of things.
 \providecommand*{\pair}[2]{ \left({#1},{#2}\right) }
 
+% A triple of things.
+\providecommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
+
 % The Cartesian product of two things.
 \providecommand*{\cartprod}[2]{ {#1}\times{#2} }
 
 % The Cartesian product of three things.
 \providecommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
 
+% The direct sum of two things.
+\providecommand*{\directsum}[2]{ {#1}\oplus{#2} }
+
+% The direct sum of three things.
+\providecommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
+
 % The factorial operator.
 \providecommand*{\factorial}[1]{ {#1}! }
 
@@ -65,3 +80,42 @@
 \providecommand*{\Cn}[1][n]{
   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 }
+
+% The space of symmetric n-by-n matrices.
+\providecommand*{\Sn}[1][n]{
+  \mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}
+
+%
+% Basic set operations
+%
+
+% The union of its two arguments.
+\providecommand*{\union}[2]{ {#1}\cup{#2} }
+
+% A three-argument union.
+\providecommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
+
+% The intersection of its two arguments.
+\providecommand*{\intersect}[2]{ {#1}\cap{#2} }
+
+% A three-argument intersection.
+\providecommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
+
+% An indexed arbitrary binary operation such as the union or
+% intersection of an infinite number of sets. The first argument is
+% the operator symbol to use, such as \cup for a union. The second
+% argument is the lower index, for example k=1. The third argument is
+% the upper index, such as \infty. Finally the fourth argument should
+% contain the things (e.g. indexed sets) to be operated on.
+\providecommand*{\binopmany}[4]{
+  \mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
+             { {#1}_{#2}^{#3}{#4} }
+             { {#1}_{#2}^{#3}{#4} }
+             { {#1}_{#2}^{#3}{#4} }
+}
+
+\providecommand*{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
+\providecommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
+\providecommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
+\providecommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }